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Abstract

We analyze the sensitivity to inertial rotations Ω of a micron scale integrated gyroscope consisting of a coupled resonator optical waveguide (CROW). We show here that by periodic modulation of the evanescent coupling between resonators, the sensitivity to rotations can be enhanced by a factor up to 109 in comparison to a conventional CROW with uniform coupling between resonators. Moreover, the overall shape of the transmission through this CROW superlattice is qualitatively changed resulting in a single sharp transmission resonance located at Ω = 0s−1 instead of a broad transmission band. The modulated coupling therefore allows the CROW gyroscope to operate without phase biasing and with sensitivities suitable for inertial navigation even with the inclusion of resonator losses.

Figures (4)

(a) Illustration of micro-resonator CROW gyroscope on planar substrate connected to a 3dB coupler with periodic modulation of evanescent coupling between resonators. (b) Schematic diagram of proposed modulation scheme for evanescent couplings κj. Note that the green and red discs represent the strength of the evanescent coupling between resonators, which alternates between weak (green) and strong (red) coupling or vice versa symmetrically about the center resonator.

(a) Transmission spectrum as a function of Sagnac phase shift per resonator ϕS for the alternating symmetric coupling modulation with κα = 0.1 and κβ = 0.01 (red line). Notice the single transmission resonance at 0 phase. For comparison the transmission through CROWs with uniform coupling constants κ = 0.01 (blue line) and κ = 0.1 (green line) are also shown. In all plots N = 13. (b) Closeup of central transmission resonance for κα = 0.01 as a function of ϕS and κβ for N = 9 rings. One can see clearly the narrowing of the resonance for increasing |κα – κβ|.

(a) Maximum value of dT/dϕS in the vicinity ϕS = 0 as a function of N for various coupling modulation strengths with weak coupling at the edges, κα ≪ κβ. Also shown is the maximum dT/dϕS for a uniform CROW with κ = 0.01 at the edge of the transmission band. In this figure
Qint−1=0. (b) The same as part (a) except that coupling is strong at the edges, κα ≫ κβ.

(a) Effect of finite Qint on the transmission resonance of the alternating symmetric coupling modulated CROW for κα = 0.01 and κβ = 0.7 for N = 11 resonators. (b) Maximum value of dT/dϕS in the vicinity ϕS = 0 as a function of N for finite Qint and coupling constants modulations κα = 0.01 and κβ = 0.3 (corresponding to Fig. 3(a)) and κα = 0.3 and κβ = 0.01 (corresponding to Fig. 3(b)). Also shown is the maximum dT/dϕS for a uniform CROW with κ = 0.01 at the edge of the transmission band. In both figures the resonators have radii R = 25μm and index of refraction n = 1.6